M
ariano J. Padilla is a native of Guatemala, and has had a 15-year
career in Computer Information, holding the position of Director of
Information Systems for an international feature film subtitle and translation
company. During his computer career, he designed fiber-optics networks
with video servers and gigabit backbone infrastructure. His return to school
marks a return to his original passions: engineering and applied physics. He
participates in the Transfer Achievement Program (TAP), and the Mathematics,
Engineering and Science Achievement program (MESA), and is a member of
the Fullerton College Honors program. He is a facilitator at Fullerton College,
where he conducts the supplemental instruction of Intermediate Algebra to
students enrolled in the TAP program. He is a student member of the American
Physical Society and the American Association for Advancement of Science.
Dr. Kathleen Hodge, president of Fullerton College, appointed him to the
Orange County Engineering Council, where he serves as a delegate to the
council representing Fullerton College. He plans to pursue a doctorate degree
in atomic theory, general theoretical involving M-Theory and string theory,
particle physics or quantum gravity/relativistic physics.
Y
uan Liu is a research scientist at the Holifield Radioactive Ion Beam
Facility (HRIBF) at Oak Ridge National Laboratory. She received
her Ph.D. in electrical engineering from Rice University in 1987. After
postdoctoral research at University of Washington in Seattle and University
of Tennessee in Knoxville, she went to Japan to join the Advanced Technology
Laboratories of Hoechst Japan in 1991. There, she was the project leader for
the development of optical chemical sensors for on-line detection of organic
pollutants in air and water. She has been at HRIBF since 1997. Her current
research interests include high efficiency ion sources that generate beams of
short-lived, unstable nuclei for nuclear physics and nuclear astrophysics
research, laser based beam purification techniques, and new techniques to
improve ion beam quality. She runs two separate experimental stations for
developing and testing ion sources.
DEVELOPMENT OF EMITTANCE ANALYSIS SOFTWARE FOR
ION BEAM CHARACTERIZATION
MARIANO J. PADILLA AND YUAN LIU
ABSTRACT
Transverse beam emittance is a crucial property of charged particle beams that describes their angular and spatial
spread. It is a figure of merit frequently used to determine the quality of ion beams, the compatibility of an ion beam
with a given beam transport system, and the ability to suppress neighboring isotopes at on-line mass separator
facilities. Generally a high quality beam is characterized by a small emittance. In order to determine and improve
the quality of ion beams used at the Holifield Radioactive Ion beam Facility (HRIBF) for nuclear physics and nuclear
astrophysics research, the emittances of the ion beams are measured at the off-line Ion Source Test Facilities. In this
project, emittance analysis software was developed to perform various data processing tasks for noise reduction, to
evaluate root-mean-square emittance, Twiss parameters, and area emittance of different beam fractions. The software
also provides 2D and 3D graphical views of the emittance data, beam profiles, emittance contours, and RMS. Noise
exclusion is essential for accurate determination of beam emittance values. A Self-Consistent, Unbiased Elliptical
Exclusion (SCUBEEx) method is employed. Numerical data analysis techniques such as interpolation and nonlinear
fitting are also incorporated into the software. The software will provide a simplified, fast tool for comprehensive emittance
analysis. The main functions of the software package have been completed. In preliminary tests with experimental
emittance data, the analysis results using the software were shown to be accurate.
program to assist with the data analysis is discussed in detail. Possible
enhancements and additions to the software are also described.
INTRODUCTION
Nuclear and particle physics experiments use charged particle
beams [1, 2]. The ability to transport the beams over long distances
and/or to focus them into small areas depends largely on the
quality of the beams; hence to have a measure of beam quality
is paramount. The quality of a particle beam is usually described
by its emittance and brightness. Ion beam emittance influences
charged particle accelerator design, operation, mass resolution,
and neighboring isotope suppression at on-line mass separator
facilities. In this paper, the method used for transverse emittance
measurement is briefly described and the development of a software
Experimental Emittance Measurement
The Ion Source Test Facility-2 (ISTF-2) is one of two off-line
facilities at the Holifield Radioactive Ion Beam Facility (HRIBF)
at Oak Ridge National Laboratory (ORNL) available to test ion
sources for on-line generation of Radioactive Ion Beams (RIBs).
The ISTF-2 consists of a high voltage platform, ion source, motor
generator, cooling system, Einzel lenses, 90° dipole magnet for
mass separation, Faraday cups for measuring beam intensities, and
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77
an emittance measurement apparatus. Figure 1 illustrates the setup
at ISTF-2.
Different methods exist to measure emittance; at ISTF-2
emittance is measured using a slit-harp device, illustrated in Figure 2,
which measures the ion beam spatial and angular distributions. The
emittance device consists of a thin slit 0.1mm wide and a detector
array, which is made up of 32 electrically isolated tungsten strips,
located down-stream of the slit. The ion beam is sampled by the
slit producing a sheet beamlet which is then allowed to drift freely
towards the detector array located 400mm (15.75 inches) away from
the slit. The slit-detector is stepped across the beam and angular
distribution measurements at each step are recorded. Thus, the beam
distribution as a function of position and angle is obtained. The
recorded data is saved in text or Microsoft Excel format. The ISTF-2
emittance measurement apparatus consists of two such step-motor
driven slit-detector units for determining the transverse emittance
of an ion beam in the x and y directions, respectively.
Einzel Lens
Mass
Analyzing
Magnet
Faraday Cup
Ion Source
Motor
Generator
High Voltage
Insulator
Faraday Cup
High-Voltage
Interlocked
Sliding Door
Fence
Figure 1. Schematic drawing of the HRIBF Ion Source Test Facility
— (ISTF-2).
Figure 2. Schematic drawing of the “Slit-Harp” emittance measuring
device.
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An emittance analysis program using the Mathematica language
has been in use; however it is limited to users who have knowledge
of Mathematica. In addition the processing time is relatively long
and requires adjustments to scripts for every emittance data file. This
study describes an Emittance Evaluation Program (EEP) developed
in Microsoft Visual Basic .net (VB.NET) for general users. EEP is
based on the previous Mathematica program and implements the
external software gnuplot [3] for 3-dimensional plots and graphs.
The software makes possible data import for text and Microsoft Excel
formats, manual background exclusion, Self-Consistent Unbiased
Elliptical Exclusion (SCUBEEx) algorithms [4] for noise reduction,
emittance calculation, visualization, and report generation. The
algorithms used within the software are discussed in detail in the
next section. EEP allows the analysis of emittance data without the
need for manual programming. The beam profile, root-mean-square
(RMS) emittance, Twiss parameters, and fractional emittances of
an ion beam are calculated simultaneously. Figure 3 and Figure
4 illustrate the features and functions of the EEP software. The
analysis results can be saved either as text or in Microsoft Word
format. The Microsoft Word format includes RMS emittance and
beam profile graphs.
Algorithms
Emittance
Measurement
Device
High Voltage
Platform
Software Design
The experimental emittance data are stored as an array of beam
intensities I(xi, x’j) measured from each detector strip at each motor
position, where xi is the ith slit position (i = 1 to N, N being the
total number of the selected slit positions), and x’j corresponds to
the divergence angle of the jth (j = 1 to 32) detector. The data are
displayed in a 3D graph, as shown in Figure 3, and in Excel style
grids for manual inspection. Before emittance evaluation, the data
are inspected manually and, if needed, subjected to background
Figure 3. A screenshot of the Result Summary page of the emittance
evaluation program. The graphs shown include a 3D plot of the raw or
filtered emittance data (upper left), the beam profile plot with Gaussian
fit (lower left), fractional emittance contours (upper right), and the RMS
ellipse (lower right). Listed on the right are the calculated 90% fractional
and RMS emittance values for the raw or filtered data and the Gaussian
fit results.
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(6)
(7)
where Itotal is the total ion beam current detected:
(8)
and (xc, x’c) is the centroid of beam distribution calculated using
the following formulas:
Figure 4. A screenshot of the SCUBBEx analysis. The plots shown
are the RMS (upper right) and 90% fractional (lower right) emittance
versus filter ellipse, and the corresponding fractions of the total ion
beam included (upper left) and excluded (lower left) by the filter ellipses.
The RMS and fractional emittance values for each filter ellipse are also
listed on the right.
subtraction using data taken under the same conditions without the
ion beam. In order to compensate for variations in beam intensity
during a particular measurement, the data set can be normalized
using the slit current obtained at each slit position. The slit-detector
assembly is driven by a 1.8° stepping motor with a minimum linear
step of 0.015mm per 0.9°. The angular step is the angle between
two adjacent strips in the emittance detector array (2.285mrad).
These constants are used in the algorithms throughout the software.
The algorithms for evaluating beam emittances in the xx’-plane are
described below. Similar algorithms hold for the yy’-plane.
The beam profile is calculated by summing, for each position
xi, the ion currents on all 32 strips and stored in an array of variables
Iprofile(xi):
(1)
Gaussian fit can be performed on the resulting beam profile
data using the following function:
(2)
where a is the baseline, b is the amplitude, c is the mean, and σ
is the standard deviation. The full width at half maximum (FWHM)
of the ion beam can then be calculated as
(3)
The calculated beam profile is displayed together with the
Gaussian fit in EEP, as shown in Figure 3.
The RMS emittance of an ion beam is defined as:
(4)
where <x2>, <x’2> and <xx’> are the second moments of the beam
distribution in the xx’-plane:
(5)
(9)
(10)
The RMS distribution can be represented by an ellipse with an
area equal to the RMS emittance multiplied by π:
(11)
where the coefficients are the Twiss parameters given by:
(12)
Equal-intensity contour graphs depicting the emittances
corresponding to given fractions of the total ion beam distribution
are also calculated. The area within each contour divided by π is taken
as the emittance for that particular beam fraction. The calculated
RMS emittance, Twiss parameters, and fractional beam emittances
for 10–90% of the total beam, together with the corresponding RMS
ellipse and emittance contour plots, are summarized in the Result
Summary page in EEP, as illustrated in Figure 3.
DISCUSSION AND CONCLUSIONS
Noise exclusion is essential for accurate determination of beam
emittance values. Non-zero background noise in emittance data
can have a large impact on the values of RMS-emittances derived
from the data. The SCUBEEx method developed by Stockli et
al. [4] is employed in EEP with slight modifications for unbiased
noise reduction. This method applies successively smaller exclusion
ellipses around the centroid of the emittance data. Any data points
falling outside of an ellipse are assumed to be background noise. The
RMS and fractional emittances are then calculated using the data
within the ellipse. Figure 4 illustrates an example of the SCUBEEx
process: the calculated RMS and 90% fractional emittances decrease
with decreasing ellipse size as more noise is excluded, reaching a flat
region where the emittance value stays relatively the same because
most of the background is excluded. When the ellipse is further
decreased the emittance values will decrease sharply as the ellipse
begins to cut out the actual ion beam. It can be seen in Figure 4,
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79
the 90% fractional emittance shows a clear plateau between ellipses
of 10–120mm-mrad, while a plateau in the RMS emittance is
reached between 10–60mm-mrad. Figure 5 presents a side-by-side
comparison of a data set prior to and after the SCUBEEx filtering.
The left graph shows the raw data with background currents, which
give a RMS emittance of 16.6π-mm-mrad. The right graph displays
the data after excluding the background current with a filter ellipse
of 120mm-mrad. It clearly shows that most of the background noise
is removed while the real beam distribution is intact. The resulting
RMS emittance is reduced to 4.3π-mm-mrad.
After SCUBEEx analysis, the RMS and 90% fractional
emittances of the ion beam are determined as the average emittance
values in the corresponding plateau or flat regions of the SCUBEEx
results. EEP allows users to easily view and select the plateau region
for final emittance evaluation. A user can examine the SCUBEEx
results shown in Figure 4 and select the emittance values in the
Figure 5. Equal-intensity contour plots generated by EEP for an
experimental emittance dataset before (left graph) and after (right graph)
noise reduction using a 120-mm-mrad filter ellipse.
plateau region using simple mouse clicks from the list supplied on the
right; the average RMS and fractional emittances and their standard
deviation are calculated from the selected values and the results are
displayed immediately, as illustrated in Figure 6.
The main functions of the software package, including data
input and visualization, data processing, SCUBEEx, emittance
evaluation, and results output, have been completed. The codes
have been tested with experimental emittance data and shown to be
accurate. During the RIA 2006 Summer School [5] held at HRIBF,
EEP was used in the Hands-on-Program on Ion Source Beam
Emittance for ion beam emittance evaluation and the analysis results
from EEP were in excellent agreement with the Mathematica results.
The installation of EEP is simple and in standard (MSI) Microsoft
Installation Package format. The EEP software package requires
the .net framework (which most computers running Microsoft XP
software have) and Microsoft Office 2003 for report and graphic
functionality.
80
Figure 6. As the final step to obtain the RMS and 90% fractional
emittance, a screenshot shows the selected plateau region (high-lighted
area) in the SCUBEEx results with the mean and standard deviations
of the selected RMS and 90% fractional emittance values displayed in
the box below..
EEP provides a simplified, fast tool for comprehensive emittance
analysis. The interactive interface of the EEP software allows the
user to easily perform emittance analysis without performing
manual calculations and formula derivations. Future EEP software
enhancements include polynomial and cubic spline interpolation of
data points, interpolated data visualization, and multiple emittance
data file capabilities for cross reference or comparison. Such
enhancements would provide additional capabilities for accurate
emittance evaluation and further simplify the emittance evaluation
of ion beams.
ACKNOWLEDGMENTS
This research was conducted at Oak Ridge National Laboratory.
I thank the U.S. Department of Energy Office of Science for allowing
me to participate in the CCI program to further my studies, broaden
my perspective on my science field, and to have a unique and highly
productive learning experience. Special thanks to my mentor Yuan
Liu for her patience, guidance, and teaching. I would also like to
thank Daniel Stracener of the Physics Division, Paul Mueller also of
the Physics Division for his advice and cordial support, and Kathy
Ketner, Cheryl Terry, and Lee Vang of the Oak Ridge Institute for
Science and Education for their organization and coordination.
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REFERENCES
[1] Stanley Humphries Jr., “Charged Particle Beams,” John
Wiley and Sons, 1990.
[2] J. Nolen and M. Portillo, “Charged Particle Optics” in The
Optics Encyclopedia – Basic Foundations and Practical
Applications, Vol. 1, Thomas G. Brown, et al. (eds.), WileyVCH, Berlin, 2003.
[3] gnuplot ver. 4.0, Peter Mikulík and Ethan Merritt, et al.
[4] M.P. Stockli, R. F. Welton, R. Keller, A. P. Letchford, R.
W. Thomae, and J. W. G. Thomason, AIP Conference
Proceedings, Volume 639, pp. 135-159, 2002.
[5] Oak Ridge Associated Universities, ”Fifth RIA Summer
School on Exotic Beam Physics”, July 2006, “http://www.
orau.org/ria/ria06/program.htm”
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